Transcript of Maths in context – embedding learning across the curriculum areas
Katherin Cartwright: Katherin here, and Chris in the background. Thanks again and welcome to join us today for Syllabus PLUS K-6 Maths. This is our second session in our five-session series around the new syllabus.
Today's session is all about embedding the learning across the curriculum areas. Just a reminder that this session today is being recorded, and will be available to participants. We'll send out an email link after the session, probably on Friday this week, that you can access the recording again if you wish, or share it with other members of your staff that aren't with us today.
Learning across the curriculum areas. This is a fairly new section of our syllabus, and it will be a section that's new for all of the first-phase syllabuses and other syllabuses that are to come that are brought out as the Australian curriculum rolls out across Australia. The purpose of the learning across the curriculum areas are to develop and relate to others as individuals. We want our students to be able to do this, and sort of become a global citizen and at least a local citizen, and to see learning as a bigger picture than just themselves in their school. It also meets the goals of the Melbourne Declaration.
We really want to promote equity and excellence in our schools, and we want our students to become successful learners who are confident and creative and informed citizens. It's really an overarching aspect of our syllabus that we haven't really had before, but it brings a really nice richness to our content.
The learning across the curriculum areas in our syllabuses for NSW incorporate a number of different aspects. They incorporate the cross-curriculum priorities, the general capabilities, and then there's also three other areas that the board has specified. Now, I've got the little icons there, and they're the icons that you'll see throughout the content of each syllabus. And today we're obviously talking about it in regards to the mathematics syllabus. So, not all of these icons are present in all of these syllabuses, so for mathematics we don't have links to civics and citizenship and difference and diversity. Now, not because they can't be linked, but they didn't want to make the links tokenistic, so there's definitely some areas that don't appear for us. I also want to point out that this is not a definitive list of where you could make connections to other KLAs or to these general capabilities or cross-curriculum priorities. It's just they're suggestions within our content and, yes, you can make other links as well if you like.
So, I mentioned those three sections. So, the Australian Curriculum, at ACARA, they talk about cross-curriculum priorities as "encouraging conversations", OK, between students, teachers and the wider community, and between learning areas as well. And that is obviously something that's going... that is encouraged in secondary schools. I guess it's a little bit easier in primary schools, where you teach all of the KLAs, whereas in high schools there needs to be planning around KLAs to meet so that you can have those conversations.
The general capabilities, which are helping students to live and work successfully in the 21st century, and I'll talk a bit more about that in a moment. And then there's those other areas that the board has deemed are really important for our students that are about contemporary issues that they face locally, nationally and globally. And we want to really develop an understanding around these, and it encompasses knowledge, skills, attitudes and behaviours.
So, just touching on 21st-century learners, I guess this is a catchphrase that's passed round a lot at the moment, but it is really an important aspect to remember. And this information here comes from the Fluency21, which is a great website, if you haven't been there before, about 21st century fluencies. There's a link at the bottom of the screen there. And it really cleared it out for me when it talked about that we want students who can think critically, communicate effectively, and it's building on a base, a core of knowledge they already have. So it's not necessarily when they're learning the new skills, it's how they're actually critically thinking about those skills and communicating it to other people. And when I hear those words "think critically" and 'communicate', straightaway I think about our Working Mathematically outcomes in the mathematics syllabus. It links straight to those, and if you were listening last week or have listened to our recording, we talked about Working Mathematically being the 'how' you teach the 'what' of the syllabus.
So, there's a whole list of 21st century learning skills, and some of them vary across different websites or resources, but they generally talk about critical thinking, problem solving, communication and collaboration. And again, these are some of those aspects that link for us to Working Mathematically outcomes.
So, we really want to make it clear that the learning across the curriculum areas, they sit in our content of the mathematics syllabus, so they kind of come context free. They might seem like great ideas to have as themes, but what we want them to be and what they're intended to be is part of the syllabus embedded in the content. So the content of mathematics, for example, provides the context with with to explore these areas.
So they need to be evident in the teaching and learning of your program, so when you developing your lessons, your unit of learning and your activities, that's where they need to be addressed. We don't just want it to be a list that you check off at the top or the beginning of your program. They're embedded in the actual content. So if that's all you take away from this afternoon, we want you to be really clear about where they sit within the syllabus. So if you're actually looking at the hard copy, if you've got it with you or you'll look at it later, you'll see that the information around learning across the curriculum areas sits after the page that says 'Content'.
There's also a really good feature of the online version of our K–10 Mathematics Syllabus is that you can filter by the learning across the curriculum areas. So, for example, I've got here that I've chosen the Mathematics K–10 Syllabus, I've chosen Stage 2 and I've chosen sustainability. So if you're looking for places within our content that could link, to sustainability in the sense that you could possibly write an integrated unit of learning, marrying up with, say, HSIE, you can actually filter through the information to see where those connections could be made. And I think this is a really useful thing to have in our syllabus. So, again, I guess we don't want to have this as our starting point, that, you know, we now want to focus on sustainability, but if it's something you're already doing within another KLA, why not see if there's any outcomes in other syllabuses that would match up as well so that your unit can cover a number of outcomes at the same time? And I think that's a great thing to encourage. Particularly in primary schools, we've used integrated learning a lot, but now we can just get another depth and another aspect to it with these learning across the curriculum areas.
So, today's session, we've only got our 30 minutes today, so we're just going to touch on a few of the learning across the curriculum areas that we feel come up the most often in mathematics, and seem to be the most important for us in mathematics. Now, each time I go through one of these learning across the curriculum areas, at the top right you'll see a discussion question. Now, we don't have time today to go through those discussion questions, but we've placed them there so that if you're watching this as the recorded version, or want to watch it again with the rest of your staff or with the stage or with a faculty, you might want to pause the recording and have a group discussion answering that question. We think it would really deepen your understanding of these learning across the curriculum areas and help you to form a shared knowledge around them across your school.
So, when we talk about critical and creative thinking, it's about students identifying similarities and differences and engaging in reasoning. Again, links to Working Mathematically - reasoning and also understanding. So we've given you an example here, and this is from 'Stage 2: Patterns and Algebra', where students are investigating and making generalisations about properties of odd and even numbers. And they need to be able to explain what happening when they make these calculations.
So, this is a sample activity from the 'Talking About Patterns and Algebra'. It was a CD. It's now a PDF. And that image at the top right there is hyperlinked, so if you want to click on it now or later on, you can go straight to that resource, which sits behind our DEC firewall, but you can download the PDF and use it. So, this lesson, it's involving a lot of questions around adding, multiplying, subtracting odd and even numbers. And I think it's the questions that really engage the students in the critical and creative thinking. So instead of just giving them the questions to do about adding and multiplying odd and even numbers, it's actually asking them to happen... To ask them, "What happens when?" or "What happens if?" And those kind of question stems are really important to engage students in critical and creative thinking. So, this is just one example of where you could use that embedded in the content.
So, as they develop these critical and creative thinking skills, students learn a lot of new skills themselves, so it's about posing questions, applying logic, looking for alternate pathways to get to the same answer, looking at possibilities, evaluating the ideas. When you hear these words used, they're very higher-order thinking skills, so we're really sort of upping the ante and setting the bar high for our students. We want them to develop these skills within the content.
So, activities that promote creative and critical thinking are innovative. They allow students to communicate what they're learning about. There's a sharing aspect. Reasoning. They have to weigh evidence and think about why they have a certain opinion, and share it with someone else, and maybe come to a shared conclusion themselves. And it's finding solutions, not just answering questions. So, there's a lot of flexibility and precision that's required when you're a critical and creative thinker. So we want them to really engage in some of those processes. And, yes, these have to be taught. Our students don't just come with this kind of ability. So if we can embed it through the questioning we're using in our classroom or the questioning we're asking our students to participate in, hopefully they'll start to think outside the box, I guess, and see different ways of solving questions.
So, the second learning across the curriculum area we thought we wanted to touch on today was sustainability. So, again, there's that question, the discussion question, so if you're watching this as a recording or you want to visit this again, you can ask that question of your stage or school group. So, for mathematics, this is linked in with data, really strongly, and it's about students engaging in investigations regarding sustainability. So, it's sort of moving away from that "Let's count the cars at the top corner of the school and the street outside the school." It's trying to get them into some of those current issues, some of those issues that are global that are beyond just their own little world, and seeing how they actually match up with real-world issues. And so the example we've used here is in Stage 2, and it's where they're actually collecting some data, and also then looking at data that's collected by others, and the purpose for which they collect data. So someone like an environmental group would collect data and statistics to be able to persuade people along their lines of thinking, or to explain the impact that certain processes or businesses are having on the environment. And we want our students to also be able to pose questions of interest, so it's engaging in their interest as well as in society's interest. And things about the environment are generally something that students can connect with, because you can see it on a local and a global scale.
So, lesson examples for this learning across the curriculum area link really strongly to HSIE, and so I chose the outcome from relationships and places, and it's about describing people's interactions with the environment. And a really good source of information for this, we thought, was 'Behind the News'. Now, a lot of people, particularly if you're a Stage 3 teacher may be familiar with 'Behind the News', the ABC's show. It's been going for quite a while. But their website is a wealth of information. They not only have the news items on there from the shows they've done, but they often have lesson plan resources attached to those. So I've put a link there to a story around the Murray-Darling basin and issues for farmers. And it doesn't necessarily say "now create some data" or "now analyse the data" that the farmers have used in this story, but I think you could add that in yourself. So it's using the information that's there and creating a lesson in mathematics around it to get that link with sustainability. There's also a really good one in there about plastic bags, OK? So that's something that I thought would be really useful for students, because they might go shopping with their parents and they see people using shopping bags, but they can then see the bigger impact on the environment beyond just their home or the classroom or their local community. You could even just search within 'Behind the News' for the word 'environment', if you're looking at sustainability, and it comes up with loads of stories that you could use in your classroom. So again, that image is a link to the 'Behind the News' website if you want to use that.
Another great resource is 'Splash ABC'. If you haven't been here, it's fantastic. They have... Obviously, for us, we've been looking at early primary and upper primary sites, and they have links for a number of different KLAs. Obviously we're looking at maths. And so I clicked on that one, and there's lots of videos that you can watch and listen to and play. They also have a huge collection of interactive learning objects. Now, most of them, or some of them, are from Education Services Australia, which used to be called the Learning Federation. And we normally access those through TaLe, but when I went and had a look on the 'Splash' website, someone's been to a lot of detail to find some really quality ones, because if you've been to Learning Federation, there's hundreds of different learning objects, and so I think they've sort of got the cream of the crop on here, so I do recommend you go and use this website. Included in this website they also have videos and stories around other KLAs, and so I found one in the upper primary section, there's one on orienteering. And there's also one on mapping the sea floor, so already I'm thinking about the links with mathematics and how that's also linking to other KLAs, that sort of integrated approach. So here's another great website. If you haven't been there, go and have a look and explore it. It's really, really useful. And I think as we're starting to look at these learning across the curriculum areas, we need to start seeing the connections between our syllabus area and other ones as well.
So, students learn how to contribute to sustainable patterns of living by investigating data around things like environmental issues. You can use other issues as well. That's just the one we've mentioned today. Measuring and evaluating–what happens changes over time, OK? Things like rainfall and garbage, there's some really good research you can look into around the litter that we, you know, may use in the school playground, where that goes and what happens on a global scale. So seeing what changes over time as our population increases, and obviously we create more garbage in our environment. There's also...we need to get them to start quantifying this impact, so how does that then affect human activity and the environment as well? And we want them to start collecting and comparing data about conditions in our world. So, they're communicating their findings, they're observing, they're engaging, they're measuring, so it's really beyond just that, you know, "let's have a look at something that's quite localised" or "let's look at hair colour or favourite sports or favourite foods" and really starting to see quality links for mathematics in the real world.
Another learning across the curriculum area that comes up a lot in mathematics is literacy. Now, obviously we have a lot of focus on word problems and problem-solving. That's one of our Working Mathematically outcomes. So, there's a whole wealth of connections in mathematics through not only mathematical vocabulary and the conventions we use for communicating maths, but even just maths in a written form, so written problems themselves. And I think I mentioned last week as well about Newman's prompts. If you're not familiar with Newman's error analysis and Newman's prompts, do a Google search. It's just looking at a way that you can work through problems. It's a five-step questioning approach. And it's really valuable to see that link with literacy in mathematics. So, here we've got an example from Stage 3, where the students have to be able to select and classify two-dimensional shapes from a description of its features. So straightaway you can see that you can look at some information. Writing. You might want to write informative text around the description of a shape. And also that they have to be able to explain the differences between regular and irregular shapes. So there's lots of talking and listening as well. I know that's a current syllabus term. But that talking around mathematics and using the language of mathematics is really, really important.
So a lesson from that - this comes straight from the 'Teaching Space and Geometry' K-6 CD. Now, this is not hyperlinked straight there, because you would have received this CD if your school participated in the registered course version of this professional learning for space and geometry. We have included this lesson and another one that I'll mention in a moment in the file pod at the end of this session today. So we've at least given you a little taster. I'm not sure, but you may still be able to access TPL for this from your region as they currently exist, maybe till the end of the year. Otherwise, we are looking at re-issuing these with links to the new syllabus in the future.
But just...this is a barrier game, where the students obviously create a pattern or a design using some shapes that's covered, and they have to explain it to their partner. So giving verbal directions about where to put it, how to replicate the design they've already got. So, there's lots of talking, and the more specific language they use, particularly around orientation and position, so prepositions, is really going to help the other student understand where they're placing the shapes. And this kind of activity's great if you can record the conversation the students have, or even sit with a couple of students while they're doing it and take some notes around what they're saying, just to get an idea of the kind of language they're using in the classroom to explain what they're trying to say.
So, students develop the skills they need to learn to communicate confidently, and they need to understand written problems and instructions as well, and also specific mathematical meanings of words that might have a different meaning elsewhere. Things like 'product' have a different meaning. 'Left' has a different meaning in different contexts. So it encompasses not only reading/writing, but also they're viewing and looking at graphs, and looking at explanations and descriptions, and reading two-way tables. There's lots of areas of mathematics where they need to have these literacy skills.
And that whole concept of metalanguages, we just want to touch on that a little bit more, just so that you have that understanding of what metalanguage is. I think sometimes people just think, Oh, I'm using mathematical terms - I'm using metalanguage." That's not really covering what metalanguage is about. So, it's talking about language, so it's not just the vocab used, it's the discussion of it, and how it's used in a mathematical context. So, a simple example, it's things like 'octagon', where the part of the word 'oct' comes from, and how you can relate that to other areas as well. So we want lessons to have high levels of talk about the language and how the language actually works. So, it's specialist terminology, not just by itself, unless you start discussing it and explaining it in I guess, you know, layman's terms non-specialist terms. So it's making it understandable for students, and helping them see why we use specific language, particularly in mathematics. So, there's also a lesson plan attached at the end of this session called 'Find a Face' also from the 'Teaching Space and Geometry' CD, and the lesson has lots and lots of questions around the mathematics required for shapes, and for two-dimensional shapes in particular. So... And three-dimensional. Does it have a link to three-dimensional? I think it might have a link to three-dimensional in there as well. So, have a look through that lesson plan and look at the questioning that's used to encourage that talking about language throughout the lesson. So it's something you need to actually plan for. It's not just going to happen. You need to write those questions in your lesson plan as well.
Another learning across the curriculum area that comes up frequently in mathematics is information and communication technology capability. I really want to stress that word 'capability'. It's not just ICT or ICT tools or using the calculator, so I think sometimes it's a bit unfortunate that for numeracy they use the icon of a calculator, because it's not what maths stands for, but obviously it's a symbol that people associate with maths. But we want to let you know and see that it's beyond that. It's their capability. It's about investigating, creating and communicating through the use of ICT tools and their capability. And it's aiding their understanding, so it's making life easier and making communication easier. So it's not just about calculators. So when it says things like "with and without digital technologies", there's obviously a lot of prerequisite skills that are going to be necessary for students to engage in that content, so you need to be very aware of that as well. So, in our example here, we've got, from Stage 3, about identifying line and rotational symmetry. And it's a really great place to have links with digital technologies in the classroom. In this case, it's not particularly around the students actually creating it themselves, but using it. But it helps you... Because it's a concept that has motion and movement, and then being able to see it and not just visualise it is really, really important.
So, our sample lesson activity is using GeoGebra. Now, if you're a high school teacher listening in today, you may already know what GeoGebra is. If you're primary, you may not. It's a great tool, and it's where you can create little applets to explain concepts. And it's mainly for teachers to use. There is a primary version, and I'm sorry the little link down the bottom is kind of covered over by our footer today, but you can still obviously click on that, it's hyperactive, where you can download the GeoGebra software onto your computer. And the little image at the top right, you can click on that. That's a hyperlink to the resources that are still in the click section of the department, and there's some great activities in there. This one that Chris made for us - Chris Robertson made, the GeoGebra applet, and Chris Francis made up the lesson to go with it. It's about symmetry in motion, so seeing where lines of symmetry exist, if a shape has rotational symmetry, and the order of rotational symmetry. So being able to show students how these things work. We did want to make a comment in there that it's really important to use concrete materials before you go to the abstract. So you might have done some other work with the students around shapes before you move into using something like a GeoGebra applet. So, we didn't want to risk coming out of the presentation today to show you how the applet actually works, but the image in the bottom right-hand corner there does link directly to the applet if you want to have a go at it later on.
We just thought we'd give you some screen shots. So it looks like this. There's a number of different shapes there. And underneath there's a little line symmetry and rotational symmetry, like a number line, I guess, with a black dot on it. And as you use the applet you can move the little black dot.
And so basically if you move the one across the top, it shows you where the lines of symmetry sit. And obviously as you move it back, they sort of disappear again.
And if you use the bar along the bottom with rotational symmetry, it shows you the shape rotating around, and so you can work out your order of rotational symmetry. So how many times the shape is identical to its original position as you rotate it 360 degrees. So if you're not familiar with GeoGebra, go and have a little explore. It's a fantastic resource that you can use. I haven't created many things in it myself yet. Chris Robertson's going to give me a few lessons. There are some really excellent help videos within there as well, and even through YouTube I found a few as well. So it might be something to explore if you've not done that before and you're interested in space and geometry. It's a great place to go.
So, students can use information and communication technology capabilities when they're creating patterns, they're gathering data, they're representing position, displaying data, measuring area. So they're trying to make something quite visual, and to help students see it from a different point of view. So, you know, students are generally pretty tech savvy, but you still have to teach these skills. Like we have to teach critical and creative thinking skills, you also have to teach them these capabilities. So you don't just want to use iPads because they're new and fun. You want to use them because they're making life easier or making the representation more realistic for our students, so they can see how things work and how shapes can be moved and how symmetry works and how mirror image works, and how 3-D objects can be manipulated to look at them from different points of view. So, there's really some wonderful ways in which you can use ICT and capabilities of ICT in the mathematics classroom.
So, some final thoughts for today. Learning across the curriculum, it's a massive area. I know we've only touched on a few of them, but hopefully it's given you a few ideas of where you can use it in your content, in your teaching. So, it exposes students to a broader, richer education experience. It's grounded in the idea of lifelong learning, so they're going to continue to learn about these different areas as they go not only through K-10, but also beyond schooling. We don't want it to be treated as an add-on. It needs to be embedded in the curriculum. It really provides a vehicle for students to talk about their work in relation to themselves and to the wider community. And you really need to have a clarified... It needs to be clarified as a whole school what the learning across the curriculum areas are so that you have a shared understanding. So, for each syllabus they're a little bit different. The information about how it's embedded in each syllabus is slightly different. So you need to have those discussions as a whole school so that everyone is clear on what it looks like for each subject area. It also creates a real-life purpose for learning. So like we talked about with the data, it's looking at real-life data, not just made-up data, for the purpose of a lesson. And it really shows that link through key learning areas as a central capability. So it's something you can develop different aspects of in different syllabuses as well as all together if you created an integrated unit.
So, that's the end of today's session. Thanks for tuning in again. There are our contact details there, for myself and for Chris. We welcome any feedback. We were very excited, the feedback we got from our first session, so thank you to everyone who has completed their evaluation from session 1.
Just going onto our conclusion screen here. Just a reminder that, yes, if you have enrolled via MyPL, we'd love you to complete the online evaluation, and that our next session is next Tuesday, 12 November, and that'll be about 'What's New: Number and Algebra'. So you can go to MyPL and just type in that event ID and you'll be able to enrol for that event as well. And we'll be sending out the recording from today's session probably this Friday or early next week. So, thanks again for tuning in, and we hope you found this afternoon's session useful, and see you next week.